Logics

Rationality has long been considered the quintessence of humankind. However, psychological experiments revealing reliable divergences in performances on reasoning tasks from normative principles of reasoning have cast serious doubt on the venerable dogma that human beings are rational animals. According to the standard picture, reasoning in accordance with principles based on rules of logic, probability theory, etc., is rational. The standard picture provides the backdrop for both the rationality and irrationality thesis, and, by virtue of the competence-performance distinction, diametrically opposed interpretations of reasoning experiments are possible. However, the standard picture rests on shaky foundations. Jean Piaget developed a psychological theory of reasoning, in which logic and mathematics are continuous with psychology but nevertheless autonomous sources of knowledge. Accordingly, logic, probability theory, etc., are not extra-human norms, and reasoners have the ability to reason in accordance with them. In this paper, I set out Piaget’s theory of rationality, using intra- and interpropositional reasoning as illustrations, and argue that Piaget’s theory of rationality is compatible with the standard picture but actually undermines it by denying that norms of reasoning based on logic are psychologically relevant for rationality. In particular, rather than logic being the normative benchmark, I argue that rationality according to Piaget has a psychological foundation, namely the reversibility of the operations of thought constituting cognitive structures.

Analogies are an important part of human cognition for learning and discovering new concepts. There are many different approaches to defining analogies and how new ones can be found or constructed. We propose a novel approach in the tradition of structure mapping using colored multigraphs to represent domains. We define a category of colored multigraphs in order to utilize some Category Theory (CT) concepts. CT is a powerful tool for describing and working with structure-preserving maps. There are many useful applications for this theory in cognitive science, and we want to introduce one such application to a broader audience. CT and the concepts used in this paper are introduced and explained. We show how the category theoretical concepts product and pullback can be used with the category of colored multigraphs to find possible analogies between domains using different requirements. The dual notion of a pullback, the pushout, is then used as conceptual blending to generate a new domain.

Inquisitive modal logic ${\mathrm{InqML}}_{⊞}$ is a natural generalization of basic modal logic, with ⊞ as a primitive modal operator. In this paper, we study the bisimulation quotients in the logic ${\mathrm{InqML}}_{⊞}$. For a given inquisitive modal model , we first show that the bisimilarity relation is an equivalence relation on W and that there is the largest bisimulation on $\mathfrak{M}$. We then define the bisimulation quotient and prove that a model is connected to its bisimulation quotient by a surjective bounded morphism. Finally, we prove that two models are globally bisimilar if and only if their bisimulation quotients are isomorphic.